Observing dominant dual-mode second-harmonic (DMSH) generation in an isotropic nonlinear elastic cylindrical waveguide

Abstract

Nonlinear ultrasonic techniques have gained much interest owing to their microstructural characterisation capabilities, which can help in early-state defect detection and provide timely maintenance activity calls. Microstructural features such as micro-cracks, precipitates or dislocations can be accessed while studying higher harmonics data via amplitude analysis. A proper understanding of second harmonic modes shall provide clarity and insights into the defect type. This paper studies and analyses the second harmonic wave modes generated while exciting fundamental torsional mode(T(0,1)) in a cylindrical wire waveguide structure. The work presents the presence of a simultaneously propagating dominant dual-mode second-harmonic (DMSH), fundamental longitudinal (l(0,1)) mode and an orthogonal-torsional (t(0,1)┴) mode generated on a cylindrical steel wire waveguide of 1 mm diameter while excited with a T(0,1) mode in a large domain. The presence of two dominant modes at second harmonic frequency is the reason for terming this phenomenon DMSH. The DMSH was observed and analysed using numerical simulations and validated experimentally. This work attempts to extend the study of DMSH generation on thin plates with SH0 mode with the analogy of cylindrical structures for rod waves with T(0,1) mode. However, in the present study of cylindrical waveguides, at primary frequency also, dual flexural modes (F(1,1)-F(1,2)) with approximately similar group velocities to DMSH were observed. These wave modes were identified with Fourier transform methods (STFT and 2D-FFT) and interpreted using dispersion curves. The dual-mode wave packets will separate in the time domain if the travel length exceeds the minimum separation distance of approximately 60 λ, depending on the variation in their respective group velocities. This approach can provide important implications for highly sensitive long-range early-state defect detection and structural health monitoring in cylindrical structures with improved insights into the generated wave modes.